On a particular highway in Nova Scotia, it is reported that the proportion of cars that exceed the speed limit is 0.15. Given this information, the probability that a sample of 250 cars will have a sample proportion below 0.12 is approximately 0.0918.

Question

Quizplus · Accepted Answer

This is a binomial distribution problem, where the sample size n=250, the success probability p=0.15, and we want to find the probability of having less than 0.12 successes (i.e. cars that exceed the speed limit). Using the normal approximation to the binomial distribution, we can calculate the z-score as:

z = (0.12 - 0.15) / sqrt(0.15 * 0.85 / 250) = -1.73

Then, we can use a standard normal cumulative distribution table (or calculator) to find the probability of having a z-score less than -1.73, which is approximately 0.0423. Therefore, the probability of having a sample proportion below 0.12 is about 0.0423, which is smaller than 0.0918. Thus, the statement is False.

On a Particular Highway in Nova Scotia, It Is Reported